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Determining the center and radius of the inscribed circle of an equilateral triangle is a fundamental concept in geometry. This process involves understanding the properties of equilateral triangles and the relationships between their sides, angles, and key points.

In conclusion, finding the incenter and inradius of an equilateral triangle is a straightforward process due to the triangle's unique properties. The incenter, located at the intersection of angle bisectors, is also the center of the incircle. The inradius, representing the circle's radius, can be easily calculated using a specific formula. Understanding these concepts is crucial for solving various geometric problems and comprehending the properties of triangles.